We present two decoding schemes for Alamouti space-time block codes (STBC) that do not require full knowledge of the received signal. Our schemes are able to decode signals directly from the received signal power, without knowledge of the signal amplitude and phase. This in turn allows for reduced susceptibility to fast fading and lower receiver complexity. Such decoding approach is not possible for the case of conventional Alamouti STBC scheme. It is shown that the proposed First Quadrant Transmission (FQT) is able to deliver the best performance on par with the conventional Alamouti STBC scheme even when the conventional scheme has full knowledge of the received signal. Our recommendations are based on the novel complex to real Alamouti STBC mapper and the sign ambiguity elimination method, both presented in this letter.